Deep observations of the dwarf elliptical (dE) galaxy NGC 1396 (MV = -16.60, Mass ˜4 × 108 M⊙), located in the Fornax cluster, have been performed with the Very Large Telescope/Multi Unit Spectroscopic Explorer spectrograph in the wavelength region from 4750 to 9350 Å. In this paper, we present a stellar population analysis studying chemical abundances, the star formation history (SFH) and the stellar initial mass function (IMF) as a function of galactocentric distance. Different, independent ways to analyse the stellar populations result in a luminosity-weighted age of ˜6 Gyr and a metallicity [Fe/H]˜ -0.4, similar to other dEs of similar mass. We find unusually overabundant values of [Ca/Fe] ˜+ 0.1, and underabundant Sodium, with [Na/Fe] values around -0.1, while [Mg/Fe] is overabundant at all radii, increasing from ˜+ 0.1 in the centre to ˜+ 0.2 dex. We notice a significant metallicity and age gradient within this dwarf galaxy. To constrain the stellar IMF of NGC 1396, we find that the IMF of NGC 1396 is consistent with either a Kroupa-like or a top-heavy distribution, while a bottom-heavy IMF is firmly ruled out. An analysis of the abundance ratios, and a comparison with galaxies in the Local Group, shows that the chemical enrichment history of NGC 1396 is similar to the Galactic disc, with an extended SFH. This would be the case if the galaxy originated from a Large Magellanic Cloud-sized dwarf galaxy progenitor, which would lose its gas while falling into the Fornax cluster.